Method of evaluating a reconstructed surface, corneal topographer and calibration method for a corneal topographer

ABSTRACT

A Method of evaluating a correspondence between a target surface and a reconstructed surface representing the target surface is described. The reconstructed surface can be constructed by processing information obtained by illuminating the target surface with a pattern of light of a stimulator source, and capturing a reflected image of the pattern of light on an image target, the method further comprising the steps of—Determine a reference image point on the image target corresponding to a reference stimulator point on the stimulator source,—Calculating for the reference image point, using the reconstructed surface, a residual representing the correspondence between the target surface and the reconstructed surface.—Displaying the residual together with the reflected image.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the National Stage of International Application No.PCT/EP2007/009666, filed Nov. 2, 2007, the contents of which isincorporated by reference herein.

FIELD OF THE INVENTION

Corneal topography

BACKGROUND

Measurement of the corneal shape is becoming a common procedure inophthalmic practice. This is done by a technique called keratoscopy.This technique allows the study of the corneal image and the interpretedimage distortions as an indication of an abnormal cornea topography. Inkeratoscopy the following elements are used: a stimulator source toilluminate a target surface (e.g. the cornea of an eye) with a patternof light and an image target arranged to receive the reflection of thelight pattern. The information from the reflection is used toreconstruct the corneal shape. One of the most commonly used stimulatorsources is the Placido ring pattern consisting of a disk withalternating black and white rings. In modern topographers, the reflectedimage of the target surface is captured by a camera and computeralgorithms are applied to process this information to reconstruct thecorneal shape. However, this procedure is not without problems. It cane.g. be noted that, when reconstructing the corneal surface, numericalalgorithms used in commercially available Placido disk topographersneglect skew ray reflections. This leads to inaccuracy in reconstructingcorneal surfaces that are not rotationally symmetric. In Placido disktopography, the corneal shape is reconstructed under the assumption thatthe reflection occurs in a meridian plane. However, this assumption isvalid only if the corneal surface is rotation-symmetric. Fornon-rotation-symmetric surfaces, skew ray reflections can occur. Thismeans that in Placido-based topography, there is ambiguity in therelationship between the stimulator source points and image pointsespecially when the cornea is not a rotationally-symmetric surface. Thisambiguity can e.g. be overcome by applying a stimulator source thatenables to establish a one-to-one correspondence between a point on thestimulator source and a point on the image. For Placido-basedtopographers, this can be implemented by modifying the stimulatorpattern to e.g. a checkerboard pattern. It can further be noted thatwhen a colour-coded pattern is used instead of the Placido pattern, asimilar correspondence between stimulator source points and image pointscan be obtained and skew ray ambiguity can be eliminated.

As explained above, topographer that are available today provide for areconstruction of the target surface (e.g. the corneal surface), usingnumerical algorithms such as surface fitting using splines or Zernikepolynomials. Until now, little attention has been given to developingtechniques that allow an easy evaluation of the accuracy of thereconstructed surface. One known technique to evaluate the correctnessof surface reconstruction algorithms is described by Halstead et al. inOptom. Vis. Sci. 1995, Vol. 72, pp. 821-827. The reconstructed cornealsurface is evaluated by calculating the surface normals of thereconstructed surface and comparing them with the angle bisector betweenincident and reflected rays for each pair of source point and imagepoint. For the correct surface these two vectors should be identical. Ifboth vectors are not identical, a residual representing the differencebetween the two vectors can be defined. In the algorithm as described byHalstead, an angle residue (corresponding to the difference between thenormal and the angle bisector) is calculated as residual. The residualcan further be used to improve the accuracy of the reconstructed surfaceby e.g. a least-squares fitting.

A drawback of the proposed method is however that it does not provide aneasy way to assess the relevance of the calculated difference betweenthe actual (target) surface and the reconstructed surface.

OBJECT OF THE INVENTION

Therefore, it is an object of the present invention to provide a methodfor evaluation of a reconstructed surface that enables to assess therelevance of the calculated difference between the actual (target)surface and the reconstructed surface in an easy manner. It is anotherobject of the present invention to provide a corneal topographer thatenables the evaluation of a reconstructed surface in an easy manner. Itis a further object of the present invention to provide a calibrationmethod for a corneal topographer.

Other objects and advantages of the present invention will becomeapparent from the description in which embodiments of the presentinvention are described.

SUMMARY OF THE INVENTION

According to an aspect of the invention, there is provided a method ofevaluating a correspondence between a target surface and a reconstructedsurface representing the target surface, the reconstructed surface beingconstructed by processing information obtained by illuminating thetarget surface with a pattern of light of a stimulator source, andcapturing a reflected image of the pattern of light on an image target,the method comprising the steps of

-   -   determining a reference image point on the image target        corresponding to a reference stimulator point on the stimulator        source,    -   calculating for the reference image point, using the        reconstructed surface, a residual representing the        correspondence between the target surface and the reconstructed        surface,    -   displaying the residual together with the reflected image,    -   evaluating the correspondence between the target surface and the        reconstructed surface from the displayed residual.

By applying this method, the accuracy of the reconstructed surface canbe assessed more easily because of the visualisation of the residualtogether with the image. By displaying the residual on the image target,one can also assess which parts of the reconstructed surface suffer fromthe largest error (or residual) and which parts have a small error. Thismay be important in case the accuracy requirement of the reconstructedsurface is not uniform. As an example, reference can be made to thereconstruction of a corneal surface using a corneal topographer. In suchan apparatus, a reconstruction of a corneal surface is determined (e.g.using a numerical algorithm), the reconstructed surface is further to beused in a subsequent surgical procedure to adjust a patients cornea e.g.by using laser technology. It will be clear to the skilled person thatin order for this procedure to be successful, the accuracy of thereconstructed surface is important and should be verified. Byvisualising the reflected image of the target (e.g. the cornealsurface), together with the residuals, the accuracy of the reconstructedsurface can be assessed by visual inspection. This visual inspection mayalso be used to determine any further steps to be taken in e.g.modifying the reconstructed surface to reduce the discrepancy betweenthe actual (target) surface and the reconstructed surface. Note that anymethod or device suitable can be applied for displaying the residualtogether with the reflected image. Both can e.g. be displayed on ascreen that receives its input from a CCD camera, the camera serving asimage target for receiving the reflected image from the target surface.Note that the image target can be any image (or picture) recording orreceiving device such as a CCD camera or a video camera. The targetsurface in general represented the subject that is examined, in case themethod is applied for examining a patients eye, the target surface cane.g. be the cornea of said eye.

The method of evaluating a correspondence between a target surface and areconstructed surface representing the target surface may equally bedescribed as comprising the steps of

-   -   illuminating the target surface with a pattern of light of a        stimulator source,    -   capturing a reflected image of the pattern of light on an image        target,    -   processing information from the previous steps to establish the        reconstructed surface,    -   determining a reference image point on the image target        corresponding to a reference stimulator point on the stimulator        source,    -   calculating for the reference image point, using the        reconstructed surface, a residual representing the        correspondence between the target surface and the reconstructed        surface,    -   displaying the residual together with the reflected image,    -   evaluating the correspondence between the target surface and the        reconstructed surface from the displayed residual.

According to another aspect of the present invention, there is provideda corneal topographer comprising

-   -   a stimulator source arranged to, in use, illuminate a target        surface with a pattern of light,    -   an image target arranged to receive the reflected image of the        target surface, the corneal topographer further comprising a        computational unit arranged to, in use,        -   construct a reconstructed surface representing the target            surface by processing information of the stimulator source            and the image received on the image target,        -   identify a reference image point on the image target            corresponding to a reference stimulator point on the            stimulator source,        -   calculate for the reference image point, using the            reconstructed surface, a residual representing the            correspondence between the target surface and the            reconstructed surface,        -   displaying the residual together with the reflected image.

A corneal topographer according to the present invention differs fromconventional topographer in that it enables a.o. a residual calculatedfrom a comparison between an actual surface (e.g. a corneal surface) anda reconstructed surface to be displayed together with the reflectedimage from the target surface. Both can e.g. be displayed together on ascreen of the topographer. As described above, such visual inspectionbeing readily available provides an easy way to assess the accuracy ofthe reconstruction, it may also be a useful tool in deciding whether ornot an adjustment of the reconstructed surface is required or not.

According to yet another aspect of the invention, there is provided acalibration method for a corneal topographer, comprising the steps of

-   -   identifying a reference image point on an image generated by        reflecting a stimulator source on a reference surface towards an        image target corresponding to a reference stimulator point,    -   calculating the coordinates of the stimulator origin point of        the reference image point by backward ray tracing from the image        point towards the reference surface and from the reference        surface towards the stimulator source,    -   establishing the geometric relationship between the reference        image point and the stimulator origin point.

In order for a corneal topographer to provide an accurate reconstructedsurface of e.g. a corneal surface, a corneal topographer needs to becalibrated; the relative position between the different components ofthe topographer need to be know. As an example, surface reconstructionalgorithms may depend on the position of the stimulator source relativeto the image target being known. In case this relative position is notknown or not sufficiently accurate, the calibration method according tothe invention can be applied. As such, inaccuracies or errors occurringduring an initial calibration by the manufacturer can be solved. Thereference surface for use with the calibration method can e.g. be asubstantially spherical surface having an knows geometry. The referencesurface may also be a corneal surface of an eye of which the geometricalproperties are known.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 schematically depicts the basic principle of corneal topography;

FIG. 2 schematically depicts a corneal topographer enabling a one-to-onecorrespondence between a stimulator point and an image point;

FIG. 3 schematically depicts the principle of backward ray tracing asapplied in an embodiment of the present invention;

FIG. 4 schematically depicts the principle of pseudo-forward ray tracingas applied in an embodiment of the present invention.

DETAILED DESCRIPTION

FIG. 1 schematically depicts a part of a stimulator source 100 arrangedto illuminate a target surface 110 (the target can e.g. be an eye). Theray of light emanating from the stimulator source is reflected on thetarget surface, the reflected ray of light is received by the imagetarget 120 which can e.g. be a CCD camera. Between the target surfaceand the image target, a lens 130 can be present.

In general, when the stimulator source does not comprise distinctfeature points, it is not possible to establish a one-to-onerelationship between a point on the stimulator source and thecorresponding projection on the image. FIG. 2 schematically depicts anarrangement that enables this correspondence. FIG. 2 schematicallydepicts a part of the stimulator source 200 arranged to illuminate atarget surface 210. The part of the stimulator source 200 as showscomprises a pattern of rectangular shapes. The different parts or shapesof the stimulator source can e.g. emit a different colour.Alternatively, the pattern can be an alternating pattern of light anddark shapes. By doing so, a one-to-one correspondence between thestimulator source and the image can be obtained for the so-calledcrossings (in the stimulator source as depicted, the crossingcorresponds to the point where the four rectangles meet) in thestimulator source. In FIG. 2, the crossing (also referred to asstimulator crossing SC) is indicated by reference number 220. As thepattern of the stimulator source is reflected on the target surface andprojected on the image target, it will be clear to the skilled personthat an image point 230 corresponding to the stimulator crossing can befound on the image 240. This image point is also referred to as thedetected crossing DC.

Whether or not such a one-to-one correspondence between a number ofstimulator source points and corresponding image points can beestablished depends on whether or not the stimulator source patterncomprises stimulator crossings that can result in identifiable crossingson the image targets. Topographers that enables such a one-to-onecorrespondence are e.g. topographers that project a checkerboardpattern, or a dartboard pattern or a colour-coded pattern.

Based on the geometric properties of the stimulator source, i.e. theposition of the source relative to the surface target, and the image onthe image target, a reconstruction of the target surface can beestablished. Different ways of achieving such a reconstructed surfaceexist, such as a curve fitting using Zernike polynomials or a fittingusing spline functions.

Once such a reconstructed surface is established (e.g. as a continuousfunction describing the height of the cornea, or the height deviationfrom a spherical surface), this can be applied by a surgeon to adjustthe shape of a patients cornea, e.g. using laser refractive surgeryprocedures. It will be clear that in such a procedure, the outcome maystrongly depend on the correspondence between the actual target surface(i.e. the cornea of an eye) and the reconstructed surface.

In case the topographer enables that such a one-to-one correspondencefor a number of feature point (or crossings) is established, this can beapplied to verify the accuracy of a reconstructed surface. One way tocheck the accuracy of the reconstructed surface is to use a back-wardtrace algorithm to trace back the origin of an image point to thestimulator source using the reconstructed surface. This procedure isillustrated in FIG. 3.

FIG. 3 schematically a stimulator source 300 and an image target 310 ofa corneal topographer. Also indicated in FIG. 3 are a stimulatorcrossing 330 and its corresponding detected crossing 340 (i.e. thelocation on the image target where a ray of light (indicated by thedotted line 350) emanating from the stimulator crossing 320 andreflected on the target surface would end up) on the image target 310.Note that the actual shape of the target surface 320 is indicated by thebroken line 360. When the detected crossing 330 is established, it canbe traced to the corresponding point (SC) on the stimulator via backwardray-tracing. In this procedure, a ray is traced back from a point on theimage through the nodal point of the lens 370 to the reconstructedtarget surface (indicated by the solid line 380 of the target surface320. The intersection point 390 on the reconstructed surface can, ingeneral, be calculated because the surface is represented by ananalytical function, e.g. as a combination of Zernike polynomials. Thecorrectness of the reconstructed surface can be evaluated by comparingthe bisector of the incident ray and reflecting ray with the normalvector on the intersection point. A difference between the two vectors(also referred to as the angle residue) is a measure for the errorbetween the actual surface and the reconstructed surface. In general,any difference between the actual trajectory of a ray of light emanatingfrom the stimulator source and its backward traced ray via thereconstructed surface, can be used as a measure indicating the accuracyof the reconstructed surface. Such a difference is referred to as aresidual.

According to an embodiment of the present invention, the residual andthe reflected image are displayed together. This provides an easy wayfor e.g. a surgeon to assess the accuracy of the reconstructed surfaceand if required, take appropriate measures to improve the reconstructedsurface.

According to an embodiment of the present invention the residualcomprises an angle residual calculated by backward tracing the referenceimage point towards the reconstructed surface and from the reconstructedsurface towards the stimulator source. The angle residual can e.g. becalculated as indicated above.

According to another embodiment of the present invention, an alternativemethod to verify the correctness of the surface reconstruction procedureis employed. The procedure is referred to as a pseudo-forward raytracing (PFRT) routine. The procedure as described in FIG. 3 is referredto as a back-ward trace algorithm because an image point (the detectedcrossing) is traced back and compared with its point of origin. Aforward ray tracing algorithm would trace the stimulator crossing to theimage, however, as there are infinitely many rays emanating from thestimulator crossing, forward ray-tracing from this point to the cornealsurface would be impossible.

To overcome this, the alternative method according to an embodiment ofthe present invention applies multiple backward ray-tracing procedures.According to an embodiment of the method, a region around each DC on theimage target is considered (in case the image target is a CCD cameraplane, the selected region can e.g. be a square region of a predefinednumber of pixels, e.g. 11×11 pixels). In such an arrangement, each pixelin this region is traced back to the stimulator source using a backwardtrace algorithm (as e.g. shown in FIG. 3). The pixel with the closestprojection to the SC is considered the pixel location of the so-calledresidual crossing RC. The distance between the residual crossing RC andthe detected crossing DC on the image plane can be considered a measureof the accuracy of the reconstructed surface (i.e., this distance can beconsidered a residual). A visualization of this procedure is shown inFIG. 4. In this figure, 5 pixel points (400) on the image plane 410 areshown: the DC (420) and 4 pixel points in the neighbourhood of the DC.When traced back, pixel 430 is found to have the closest projection(440) to the SC 450 on the stimulator source 460. Thus, pixel 430 isconsidered as the residual crossing RC. Note that, for clarity, thedistance between the pixels, nor the distance to the target surface orstimulator source is not up to scale with the target surface. Note alsothat the reconstructed surface that is used for backward tracing thedifferent pixels is not separately shown in FIG. 4.

As will be apparent, the proposed method equally provides thepossibility of displaying residual information about the accuracy of thereconstructed surface together with the reflected image. Such anon-screen evaluation of the residual (or residual information) togetherwith the image enables an easy assessment of reconstructed surface. Asthe residual information can be shown together with the reflected imageof e.g. the patients eye, one can assess whether or not thereconstructed image is sufficiently accurate, based on the size of theerror (measured in e.g. a number of pixels) and the location of theerror.

Regarding the latter aspect, it will be clear to the skilled person thata certain error of the reconstructed surface can be acceptable oncertain locations of the cornea whereas the same error is unacceptableon other locations. The proposed evaluation method therefore providesthe possibility of easily assessing in which areas the reconstructedsurface needs further improvement.

A further advantage of the proposed method is that the amplitude of theerror (e.g. the distance in pixels between the residual crossing RC andthe detected crossing DC is found to be proportional to the cornealheight accuracy. Depending on a.o. the pixel size, one can establish therelationship between the error at a certain location on the image plane(expressed in pixels) and the height accuracy (i.e. the distance betweenthe actual (corneal) surface and the recomputed surface in a directionperpendicular to the surface) at that location. As an example, an errorof e.g. one pixel may correspond to an height error of 1 micron. Basedon this relationship, the proposed alternative method provides a furtherpossibility to easily assess whether a certain error is acceptable ornot.

According to yet a further embodiment of the present invention, theresidual information obtained by the PERT algorithm (as indicated inFIG. 4) or the backward trace algorithm (as explained in FIG. 3) is usedto further improve the accuracy of the reconstructed surface. As such,the method of evaluating the correspondence between a target surface anda reconstructed surface representing the target surface may comprise thestep of modifying the reconstructed surface based on calculatedresidual.

As an example, it is assumed that the target surface is reconstructedusing the well-known Zernike polynomials. A combination of thesepolynomials (i.e. a summation of the different polynomials weighted bymultiplying each polynomial with a corresponding Zernike coefficient)can be used to represent the target surface (e.g. the height of acornea) as an analytical function. The required coefficients for theweighing of the Zernike polynomials can e.g. be obtained from aleast-squares fitting routine. Because initially the surface is unknown,the initial Zernike coefficients can be set equal to zero, describing aflat surface. For each detected crossing on the image, an angle residuecan be calculated as the difference between a normal vector (at theintersection point) and an angle bisector between incident and reflectedray, see FIG. 3. The calculated angle residues (or residuals) can thenbe used in a least-squares fitting procedure to determine a better modelfor the surface.

As will be clear to the skilled person, the residual of the detectedcrossings as obtained from the PRFT algorithm can equally be applied ina least-squares fitting routine for obtaining an improved surface.Compared to the use of the angle residues in an optimisation (or furtherimprovement) routine, the use of the residuals of the PRFT algorithmprovides the following advantages:

-   -   as there is a known relationship between the residual (e.g.        expressed in a number of pixels or pixel size) and the height        accuracy (as explained above), the calculated residuals can be        used to determine whether the optimisation process can be        stopped or whether a further iteration is required. In case the        residual values are below a certain value, one can easily        determine the corresponding height accuracy. Alternatively, one        can require a certain height accuracy (e.g. an corneal height        error less than 1 micron) and determine the corresponding        allowable residual value. This value can be used in the surface        optimisation procedure as a criterion to stop or continue the        procedure.    -   As the FRET algorithm also provides information as to where the        errors occurs on the corneal surface, a weight function can be        applied to the residuals such that an improvement in a next        iteration focuses on the areas where an error is least        acceptable.

It can further be noted that such a weight function may also be appliedto suppress the contribution of large residuals (mainly outliers) in thefitting procedure.

The PFRT method as described above has been applied to measurements offive different surfaces:

(1) a PMMA (polymethyl methacrylate) spherical surface with 6.99 mmradius of curvature.

(2) a PMMA spherical surface with 9.00 mm radius of curvature.

(3) a PMMA toric surface with maximum axial radius of curvature of 8.02mm and minimum axial radius of curvature of 7.05 mm.

(4) a human cornea, from the left eye of a 38-year-old man, with noknown abnormality, and (5) a human cornea, from the left eye of a61-year-old man, with subepithelial infiltrate.

As described, the PFRT method can produce residual information in pixelunits of the reconstructed surface on the image (e.g. a CCD image)itself. To produce an accurate description of the corneal surface, twothings must happen. First, the location of the image crossings (detectedcrossings DC) must be determined accurately. Second, the numericalreconstruction of the corneal surface must be consistent with the DCs.The output of the PFRT routine is an indicator whether the secondprocedure was implemented well. It will be clear to the skilled personthat the accuracy of the first procedure (obtaining the position of thedetected crossings DC) is important to obtain a reliable output of thePFRT procedure or any other evaluation method. In this respect,reference can be made to Spoelder H J W, Vos F M, Petriu E M, Groen F CA. Some aspects of pseudo random binary array-based surfacecharacterization. IEEE Trans. Instrum. Meas. 2000; 49:1331-6 showingthat a subpixel accuracy in detecting the location of image crossings DCcan be obtained. In case a 1 pixel would correspond to an heightaccuracy of 1 micron, the PFRT procedure can result in a submicrometercorneal height accuracy when the optimisation is continued until thecalculated residuals are less than 1 pixel. In this respect, it is worthmentioning that the accuracy that can be obtained also depends on thecomplexity of the actual surface combined with the degrees of freedom ofthe surface fitting function. It has been shown that the overallresidual (or mean residual of the detected crossings) increases withcomplexity of the measured surface. The residuals were found to be thesmallest for the artificial surfaces; the spherical surfaces (1) and (2)resulted in a mean residual of 0.70 pixel, the toric surface (3)resulted in a mean residual of 0.81 pixel. The regular cornea (4) wasfound to have a slightly higher residual compared with the artificialsurfaces (a mean residual of 1.16 pixel). This effect is found to becaused by the effect of higher order shape features. However, becausethese shape features are not as dominant when compared with thespherical and toric shape features, the effect on the residual was foundto be relatively small. Whereas, for the irregular cornea (5), theeffect of the higher-order shape features is larger, thus producing anincrease in the mean value of the residual (a mean residual of 2.94pixel was found when the surface was modelled using Zernike polynomialsuntil radial order 6). The accuracy of the surface reconstruction wasfound to improve when the Zernike radial order used to model the cornealsurface is increased. The addition of more Zernike components enablesbetter fitting of the local surface features. For the artificialsurfaces, a lower radial order for the Zernike expansion (order 6) issufficient to reconstruct the surface with subpixel accuracy. For theregular cornea, subpixel accuracy was observed only for Zernike radialorder of 10 or higher. For the irregular cornea (5), order 20 was foundstill not sufficient to produce subpixel accuracy for the surfacereconstruction. Nevertheless, at this order the accuracy was found toapproach pixel resolution, which is reasonable enough for clinicalpractice. The above also indicates that to some extent the use ofZernike polynomials will produce accurate corneal surface reconstructionas long as a sufficient radial order is used.

It should be noted that the PRFT routine as described does not depend onthe way the reconstruction of the surface is done. It will be clear tothe skilled person that any surface fitting procedure can be applied toprovide a reconstructed surface. This reconstructed surface can then beevaluated using the PFRT routine as described and/or can be furtheroptimised using the outcome of the PFRT routine (i.e. the residualinformation).

According to an embodiment of the present invention, there is providedin a corneal topographer that enables an evaluation of a reconstructedsurface as described above. In order to do so, the corneal topographercomprises a computational unit arranged to

-   -   construct a reconstructed surface representing the target        surface by processing information of the stimulator source of        the topographer and the image received on the image target of        the topographer,    -   identify a reference image point on the image target        corresponding to a reference stimulator point on the stimulator        source,    -   calculate for the reference image point, using the reconstructed        surface, a residual representing the correspondence between the        target surface and the reconstructed surface,    -   display the residual together with the reflected image.

As will be clear from the above, various way or determining thereconstructed surface or the residual can be applied in such acomputational unit. It can further be noted that, in order to identify areference image point on the image target of the topographercorresponding to a reference stimulator point on the stimulator sourceof the topographer, various types of stimulator sources can be applied.Examples of such stimulator sources are sources who provide acheckerboard (or dartboard) pattern of light or a colour coded patternof light. Such a pattern can be obtained by applying differenthue-values for the different area's of the pattern, or a differentbrightness or intensity. A colour coded pattern can be compared to acheckerboard that used areas of different colours as alternative to orin addition to areas that are black or white (i.e. dark and light). Thevarious areas of different colours can be arranged in such manner that areference image point on the image target of the topographercorresponding to a reference stimulator point on the stimulator sourceof the topographer can be found more easily.

According to an embodiment of the present invention, a calibrationmethod for a corneal topographer is provided. As explained above, anaccurate construction of the reconstructed surface relies on accurateknowledge of the relative position of stimulator source and imagetarget. In order to obtain this knowledge, the topographer can be usedwith a reference surface as target surface, rather than an unknownsurface. Assuming the reference surfaces geometry is known, acorresponding reconstructed surface is also known. Applying any of thetracing routines as explained above on such a surface, should result ina residual substantially equal to zero. If a non-zero residual is found,this means that the initial assumption regarding the geometricrelationship between the stimulator source and the image target wasincorrect. As the reconstructed surface corresponds provides an accuraterepresentation of the reference surface, backward ray tracing thereference image point towards the stimulator source (via thereconstructed surface) enables the actual co-ordinates of the referencestimulator point (relative to the image target) to be determined. Assuch, the actual position of the reference stimulator point relative tothe corresponding reference image point can be established. It will beclear to the skilled person that in order to obtain the relativeposition between the stimulator source and the image target in all 6degrees of freedom, the calibration can be performed for a plurality ofreference stimulator points.

Although the examples that are described relate in particular to cornealtopography, it can be stated that the methods as described (either thecalibration method or the method for evaluating a reconstructed surface)may also be applied in other field of technology where accurateknowledge of the shape of a target surface is required. An example ofsuch a field being semiconductor technology wherein an accurateknowledge of the surface characteristics of a substrate (such as awafer) is required. Another field where the described methods may beapplied is biometrical identification using e.g. an iris scan.

It can further be stated that the method of evaluating thecorrespondence between a target surface and a reconstructed surfacerepresenting the target surface may advantageously be combined with thecalibration method as described. Since the calibration method enables anaccurate determination of the geometrical relationship between thevarious components of the topographer, it may be advantageous to applythis calibration prior the reconstructed surface evaluation method asthe geometric relationship between the stimulator source and the imagetarget is used in determining the reconstructed surface.

1. Method of evaluating a correspondence between a target surface and areconstructed surface representing the target surface, the reconstructedsurface being constructed by processing information obtained byilluminating the target surface with a pattern of light of a stimulatorsource, and capturing a reflected image of the pattern of light on animage target, the method comprising the steps of determining a referenceimage point on the image target corresponding to a reference stimulatorpoint on the stimulator source, calculating for the reference imagepoint, using the reconstructed surface, a residual representing thecorrespondence between the target surface and the reconstructed surface,displaying the residual together with the reflected image, andevaluating the correspondence between the target surface and thereconstructed surface from the displayed residual.
 2. Method accordingto claim 1 wherein the residual comprises an angle residual calculatedby backward tracing the reference image point towards the reconstructedsurface and from the reconstructed surface towards the stimulatorsource.
 3. Method according to claim 1 wherein the step of calculatingthe residual comprises the steps of calculating a plurality ofstimulator points corresponding to a plurality of image points near thereference image point by backward tracing the image points towards thereconstructed surface and from the reconstructed surface towards thestimulator source, selecting the image point who's correspondingstimulator point is closest to the reference stimulator point as thereconstructed reference image point origin, establish a residual fromthe difference between the reference image point and the reconstructedreference image point origin.
 4. Method according to claim 2 wherein theconstruction of the reconstructed surface comprises a surface fittingusing Zernike Polynomials.
 5. Method according to claim 2 wherein theconstruction of the reconstructed surface comprises a surface fittingusing spline functions.
 6. Method according to claim 1 furthercomprising the step of modifying the reconstructed surface based oncalculated residual.
 7. Method according to claim 6 wherein the step ofmodifying the reconstructed surface comprises a least-squares fitting.8. Method according to claim 1 wherein the target surface is a cornealsurface of an eye.
 9. Corneal topographer comprising a stimulator sourcearranged to, in use, illuminate a target surface with a pattern oflight, an image target arranged to receive the reflected image of thetarget surface, the corneal topographer further comprising acomputational unit arranged to, in use, construct a reconstructedsurface representing the target surface by processing information of thestimulator source and the image received on the image target, identify areference image point on the image target corresponding to a referencestimulator point on the stimulator source, calculate for the referenceimage point, using the reconstructed surface, a residual representingthe correspondence between the target surface and the reconstructedsurface, and display the residual together with the reflected image. 10.Corneal topographer according to claim 9 wherein the computational unitis arranged to calculate the residual by selecting a region on the imagetarget surrounding the reference image point, calculating thecorresponding stimulator origin point for a plurality of image pointsinside the region using back-ward tracing from the image point towardsthe reconstructed surface and from the reconstructed surface towards thestimulator source, select the image point who's corresponding stimulatororigin point is closest to the reference stimulator point as thereconstructed reference image point origin, and establish the residualfrom the difference between the reference image point the referenceimage point and the reconstructed reference image point origin, 11.Corneal topographer according to claim 9 wherein the stimulator sourceis arranged to illuminate the target surface with a checkerboardpattern.
 12. Corneal topographer according to claim 9 wherein thestimulator source is arranged to illuminate the target surface with acolour-coded pattern.
 13. Corneal topographer according to any of claim9 wherein the computational unit is further arranged to perform the stepof modifying the reconstructed surface based on the calculated residual.14. Corneal topographer according to claim 13 wherein the modificationstep includes a least squares fitting based on the calculated residual.15. Corneal topographer according to claim 9 wherein the construction ofthe reconstructed surface comprises performing a fitting using ZernikePolynomials.
 16. Conical topographer according to claim 9 wherein theconstruction of the reconstructed surface comprises performing a fittingusing spline functions.
 17. Conical topographer according to claim 9wherein the image target comprises an image receiving device such as aCCD camera or a video camera.
 18. Calibration method for a conicaltopographer, comprising the steps of identifying a reference image pointon an image generated by reflecting a stimulator source pattern on areference surface towards an image target corresponding to a referencestimulator point, calculating the coordinates of the referencestimulator point of the reference image point by backward ray tracingfrom the image point towards the reference surface and from thereference surface towards the stimulator source, and establish thegeometric relationship between the reference image point and thereference stimulator point.
 19. Method according to claim 1 wherein themethod is preceded by the calibration method according to claim
 18. 20.Corneal topographer according claim 9 wherein the computational unit isfurther arranged to, in use, perform the calibration method according toclaim 18.